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Chapter 0: Problem 14

Find each sum or difference. $$ -17+9 $$

Short Answer

Expert verified
-8

Step by step solution

01

Identify the numbers

First, identify the numbers involved in the problem. Here, the numbers are -17 and 9.
02

Understand the operation

The operation required is addition. Since one of the numbers is negative, it effectively becomes a subtraction problem: -17 + 9.
03

Subtract the absolute values

Take the absolute values of -17 and 9, which are 17 and 9 respectively. Subtract the smaller absolute value from the larger one: 17 - 9 = 8.
04

Determine the sign of the result

Since the absolute value of the negative number (17) is larger than the absolute value of the positive number (9), the result will take the sign of the larger absolute value's original number. In this case, it's -17, so the result is -8.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Negative Numbers
Let's explore negative numbers a bit more since they can be confusing. Negative numbers are those less than zero and are typically written with a minus sign (-) in front of them. For instance, -17 means 17 units to the left of zero on the number line.
When dealing with negative numbers, remember a couple of crucial points:
  • Adding a negative number is like subtracting its absolute value: For example, -5 + 3 is the same as 3 - 5.
  • Subtracting a negative number is like adding its absolute value: For example, 4 - (-2) is the same as 4 + 2.
It's essential to understand these basics because negative numbers often appear in various math problems. Practicing them can significantly improve your arithmetic skills.
Absolute Values
The absolute value of a number represents its distance from zero on the number line, regardless of direction. For example, the absolute value of both 7 and -7 is 7, written as \(|7| = 7\) and \(|-7| = 7\).
Here's why absolute values matter:
  • They transform negative numbers into positive ones, making calculations simpler.
  • When adding or subtracting, you often need to compare absolute values to figure out the correct operation.
In our problem, we have \-17\ and 9. Their absolute values are 17 and 9, respectively. By subtracting the smaller absolute value (9) from the larger one (17), we find the result more easily.
Result Sign Determination
Determining the sign of the result is a crucial step in operations involving negative numbers. The rule is simple: The sign of the result will be the same as the sign of the number with the largest absolute value.
Let's break it down:
  • First, identify the absolute values: In our case, 17 (from -17) and 9.
  • Compare the absolute values: 17 is larger than 9.
  • The original number with the largest absolute value is -17, which is negative.
Hence, our result takes the negative sign, making it -8. This straightforward rule can help you quickly determine the sign in various arithmetic problems.

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Most popular questions from this chapter

Write each fraction as a decimal. For repeating decimals, write the answer by first using bar notation and then rounding to the nearest thousandth. See Example 11. $$ \frac{15}{4} $$

Frank's grandson was asked to evaluate the following expression. \(9+15 \div 3\) Frank gave the answer as \(8,\) but his grandson gave the answer as \(14 .\) The grandson explained that the answer is 14 because of the "Order of Process rule," which says that when evaluating expressions, we proceed from right to left rather than left to right. (Note: This is a true story.) (a) Whose answer was correct for this expression, Frank's or his grandson's? (b) Was the reasoning for the correct answer valid? Explain.

Solve each problem. The amount, in billions of dollars, that Americans spent on their pets from 2003 to 2016 can be approximated by substituting a given year for \(x\) in the following expression. $$2.493 x-4962$$ (Data from American Pet Products Manufacturers Association.) Find the amount spent in each year. Round answers to the nearest tenth. (a) 2003 (b) 2010 (c) 2016 (d) How did the amount Americans spent on their pets change from 2003 to \(2016 ?\)

Write each percent as a fraction. Give answers in lowest terms. See Example 13. $$ 2 \% $$

The distributive property can be used to mentally perform calculations. $$\begin{array}{l}38 \cdot 17+38 \cdot 3 \\\=38(17+3) \\\=38(20) \\\=760\end{array} $$Use the distributive property to calculate each value mentally. $$ 58 \cdot \frac{3}{2}-8 \cdot \frac{3}{2} $$
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